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Which of these choices show a pair of equivalent expression? Check all that apply.

Which of these choices show a pair of equivalent expression? Check all that apply-example-1

2 Answers

2 votes

Answer:

C and D

Explanation:

using the rules of exponents

A


125^(3/7) =
\sqrt[7]{125^3}
\sqrt[3]{125^7}

B

(
√(12))^7 =
12^(7/2)
12^(1/7)

C

(
√(4))^5 =
4^(5/2) ← correct

D

(
√(8))^9 =
8^(9/2) ← correct


User GalacticCowboy
by
8.2k points
6 votes

Answer: The correct options are

(C)
4^(5)/(2)~~\textup{and}~~(√(4))^5.

(D)
8^(9)/(2)~~\textup{and}~~(√(8))^9.

Step-by-step explanation: We are to select the correct pairs that shows equivalent expressions.

We will be using the following property of exponents and radicals :


(\sqrt[b]{x})^a=x^(a)/(b).

Option (A) :

The given expressions are


(\sqrt[3]{125})^7~~\textup{and}~~125^(3)/(7).

We have


(\sqrt[3]{125})^7=125^(7)/(3)\\eq 125^(3)/(7).

So, the expressions are not equivalent and option (A) is incorrect.

Option (B) :

The given expressions are


12^(1)/(7)~~\textup{and}~~(√(12))^7.

We have


12^(1)/(7)=\sqrt[7]{12},\\\\(√(12))^7=12^(7)/(2).

So,


12^(1)/(7)\\eq (√(12))^7.

Therefore, the expressions are not equivalent and option (B) is incorrect.

Option (C) :

The given expressions are


4^(5)/(2)~~\textup{and}~~(√(4))^5.

We have


(√(4))^5=4^(5)/(2)

Therefore, the expressions are equivalent and option (C) is correct.

Option (D) :

The given expressions are


8^(9)/(2)~~\textup{and}~~(√(8))^9.

We have


(√(8))^9=8^(9)/(2)

Therefore, the expressions are equivalent and option (D) is correct.

Thus, (C) and (D) are the correct options.

User Marco Biscaro
by
8.4k points

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